Zobrazeno 1 - 10
of 131
pro vyhledávání: '"Welch, Amanda"'
Autor:
Ballantine, Cristina, Welch, Amanda
We consider the number of various partitions of $n$ with parts separated by parity and prove combinatorially several inequalities between these numbers. For example, we show that for $n\geq 5$ we have $p_{od}^{eu}(n)
Externí odkaz:
http://arxiv.org/abs/2406.00139
Autor:
Adams, Ashleigh, Elder, Jennifer, Lafrenière, Nadia, McNicholas, Erin, Striker, Jessica, Welch, Amanda
We perform a systematic study of permutation statistics and bijective maps on permutations using SageMath to search the FindStat combinatorial statistics database to identify apparent instances of the cyclic sieving phenomenon (CSP). Cyclic sieving o
Externí odkaz:
http://arxiv.org/abs/2402.16251
Autor:
Welch, Amanda Renee
Given a finite Weyl group W_fin with root system Phi_fin, one can create the affine Weyl group W_aff by taking the semidirect product of the translation group associated to the coroot lattice for Phi_fin, with W_fin. The double affine Weyl semigroup
Externí odkaz:
http://hdl.handle.net/10919/89366
Autor:
Ballantine, Cristina, Welch, Amanda
Partitions with even (respectively odd) parts distinct and all other parts unrestricted are often referred to as PED (respectively POD) partitions. In this article, we generalize these notions and study sets of partitions in which parts with fixed re
Externí odkaz:
http://arxiv.org/abs/2308.06136
Autor:
Ballantine, Cristina, Welch, Amanda
PED partitions are partitions with even parts distinct while odd parts are unrestricted. Similarly, POD partitions have distinct odd parts while even parts are unrestricted. Merca proved several recurrence relations analytically for the number of PED
Externí odkaz:
http://arxiv.org/abs/2308.06123
Interval-closed sets of a poset are a natural superset of order ideals. We initiate the study of interval-closed sets of finite posets from enumerative and dynamical perspectives. In particular, we use the generalized toggle group to define rowmotion
Externí odkaz:
http://arxiv.org/abs/2307.08520
Publikováno v:
Mathematics of Computation 93 (2024), no. 346, 921-976
In this paper, we perform a systematic study of permutation statistics and bijective maps on permutations in which we identify and prove 122 instances of the homomesy phenomenon. Homomesy occurs when the average value of a statistic is the same on ea
Externí odkaz:
http://arxiv.org/abs/2206.13409
Autor:
Ballantine, Cristina, Welch, Amanda
Publikováno v:
In Discrete Mathematics November 2024 347(11)
Autor:
Ballantine, Cristina, Welch, Amanda
The original Beck conjecture, now a theorem due to Andrews, states that the difference in the number of parts in all partitions into odd parts and the number of parts in all strict partitions is equal to the number of partitions whose set of even par
Externí odkaz:
http://arxiv.org/abs/2101.06260
Autor:
Ballantine, Cristina, Welch, Amanda
Let $\mathcal O_r(n)$ be the set of $r$-regular partitions of $n$, $\mathcal D_r(n)$ the set of partitions of $n$ with parts repeated at most $r-1$ times, $\mathcal O_{1,r}(n)$ the set of partitions with exactly one part (possibly repeated) divisible
Externí odkaz:
http://arxiv.org/abs/2011.08220